March 5

Plan:

• Questions
• Homeword due - remember to collect it
• Sophie Germain's contribution to progress on the Fermat conjecture

Student Questions: None

What we actually did

• Questions (none)
• The Pythagorean theorem is equivalent to the assertion that areas of similar figures scale as the square of the linear dimensions
• What would life be like - and what kind of geometry would the Greeks have invented (discovered?) if the world we live in were actually hyperbolic at human scale?
• Started thinking about factoring $x^n \pm y^n$ as prepartation for studying historical attacks on the Fermat Conjecture (Euler, Germain, Lame, Kummer) using ideas that developed into contemporary abstract algebra. (This will be hard to write notes for - let's see what you produce)

The discussion page can be found here, for observations and remarks.